Orbital degeneracy loci II: Gorenstein orbits

Vladimiro Benedetti (1) , Sara Angela Filippini (2) , Laurent Manivel (3) , Fabio Tanturri (4)

1 I2M - Institut de Mathématiques de Marseille
2 Department of Mathematics [Imperial College London]
3 IMT - Institut de Mathématiques de Toulouse UMR5219
4 LPP - Laboratoire Paul Painlevé - UMR 8524

In [BFMT17] we introduced orbital degeneracy loci as generalizations of degeneracy loci of morphisms between vector bundles. Orbital degeneracy loci can be constructed from any stable subvariety of a representation of an algebraic group. In this paper we show that their canonical bundles can be conveniently controlled in the case where the affine coordinate ring of the subvariety is Gorenstein. We then study in a systematic way the subvarieties obtained as orbit closures in representations with finitely many orbits, and we determine the canonical bundles of the corresponding orbital degeneracy loci in the Gorenstein cases. Applications are given to the construction of low dimensional varieties with negative or trivial canonical bundle.

Domaines: Géométrie algébrique [math.AG]

Vladimiro Benedetti, Sara Angela Filippini, Laurent Manivel, Fabio Tanturri. Orbital degeneracy loci II: Gorenstein orbits. International Mathematics Research Notices, 2018, ⟨10.1093/imrn/rny272⟩. ⟨hal-01714766⟩